# Thread: Algebra for debt ratios in Economics

1. ## Algebra for debt ratios in Economics

Could do with a little help sorting out how these algebraic manipulations come about. I'm studying economics but my algebra is not good enough to work this out.

There are subscripts which represent different time periods which will appear as full size digits as I don't know how to use the proper notation for this site:

1. (D0(1+r) - FS/Y0(1+g)) - D0/Y0

2. = (D0(r-g)/Y0(1+g)) - FS/(Y0(1+g))

Any pointers about how the transformation of 1. into 2. is done much appreciated.

2. ## Re: Algebra for debt ratios in Economics

I suspect you have a typo in line 1. What you wrote is this:

$( D_0(1+r) - \frac {F_s}{Y_0(1+g)} )-\frac {D_0}{(Y_0}$

I think what you meant to write is this:

$\frac {D_0(1+r) - F_s}{Y_0(1+g)} - \frac {D_0}{Y_0}$

Start by making combining the two fractions, using Y_0(1+g) the denominator - this requires multiplying both numerator and denominator of the second term by (1+g), making that second term $\frac {D_0(1+g)}{Y_0(1+g)}$:

$\frac {D_0(1+r) - F_s - D_0(1+g)}{Y_0(1+g)}$

Then simplify:

$\frac {D_0 + D_0r - F_s - D_0 - D_0g}{Y_0(1+g)}$

$= \frac {D_0r - D_0g - F_s}{Y_0(1+g)}$

$= \frac {D_0(r-g) - F_s}{Y_0(1+g)}$

3. ## Re: Algebra for debt ratios in Economics

Thanks ChipB-help much appreciated